$A$ system is changed from state $A$ to state $B$ by one path and from $B$ to $A$ by another path. If $E_1$ and $E_2$ are the corresponding changes in internal energy,then:

$A$ gas expands from a volume of $1 \ m^{3}$ to a volume of $2 \ m^{3}$ against an external pressure of $10^{5} \ Nm^{-2}$. The work done by the gas will be

An ideal gas undergoes a cyclic transformation starting from the point $A$ and coming back to the same point by tracing the path $A$ $\rightarrow B$ $\rightarrow C$ $\rightarrow D$ $\rightarrow A$ as shown in the three cases above. Choose the correct option regarding $\Delta U$.

One mole of an ideal gas at $300 \ K$ is expanded isothermally from an initial volume of $1 \ L$ to $10 \ L$. The change in internal energy for this process is ....... $cal$ $(R = 2 \ cal \ mol^{-1} \ K^{-1})$

The internal energy change when a system goes from state $A$ to $B$ is $40 \, kJ/mol$. If the system goes from $A$ to $B$ by a reversible path and returns to state $A$ by an irreversible path,what would be the net change in internal energy?

$A$ system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in the figure. If $\Delta U_1$ and $\Delta U_2$ are the changes in internal energies in the processes $I$ and $II$ respectively,then: